A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting by - Maths - Pair of Linear Equations in Two Variables

Question

A two digit number is obtained by either multiplying the sum of
the digits by 8 and then subtracting by 5 or by multiplying the
difference of the digits by 16 and then adding 3 Find the
number

Ajanta Trivedi · Accepted Answer

let the unit digit and the ten's digit of the number be x and y respectively.

therefore the number = 10y + x.

sum of digits = x+y

$10 y + x = 8 (x + y) - 5 10 y + x = 8 x + 8 y - 5 7 x - 2 y = 5........... (1)$

difference of the digits = y-x [if x < y]

$10 y + x = 16 (y - x) + 3 10 y + x = 16 y - 16 x + 3 17 x - 6 y = 3............ (2)$

multiply eq(1) by 3 and subtracting eq(2):

$21 x - 6 y = 15 17 x - 6 y = 3 4 x = 12 x = \frac{12}{4} = 3$

substitute x =3 in eq(1):

$7 * 3 - 2 y = 5 2 y = 21 - 5 2 y = 16 y = \frac{16}{2} = 8$

thus the unit digit of the number is 3 and ten's digit is 8.

thus number is 83.

hope this helps you.

cheers!!

A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting by 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.